1,999 research outputs found
Quantum Mechanics and Stochastic Mechanics for compatible observables at different times
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum
Mechanics in presence of non-interacting subsystems. In both cases, it is shown
that correlations at different times of compatible position observables on
stationary states agree with Quantum Mechanics only in the case of product wave
functions. By appropriate Bell-like inequalities it is shown that no classical
theory, in particular no stochastic process, can reproduce the quantum
mechanical correlations of position variables of non interacting systems at
different times.Comment: Plain Te
Epistemic and Ontic Quantum Realities
Quantum theory has provoked intense discussions about its interpretation since its pioneer days. One of the few scientists who have been continuously engaged in this development from both physical and philosophical perspectives is Carl Friedrich von Weizsaecker. The questions he posed were and are inspiring for many, including the authors of this contribution. Weizsaecker developed Bohr's view of quantum theory as a theory of knowledge. We show that such an epistemic perspective can be consistently complemented by Einstein's ontically oriented position
Analysing singularities of a benchmark problem
The purpose of this paper is to analyze the singularities of a well known
benchmark problem ``Andrews' squeezing mechanism''. We show that for physically
relevant parameter values this system admits singularities. The method is based
on Gr\"obner bases computations and ideal decomposition. It is algorithmic and
can thus be applied to study constraint singularities which arise in more
general situations.Comment: 30 pages, 18 figures (yet small files), submitted to Multibody System
Dynamic
Tropicalization of classical moduli spaces
The image of the complement of a hyperplane arrangement under a monomial map
can be tropicalized combinatorially using matroid theory. We apply this to
classical moduli spaces that are associated with complex reflection
arrangements. Starting from modular curves, we visit the Segre cubic, the Igusa
quartic, and moduli of marked del Pezzo surfaces of degrees 2 and 3. Our
primary example is the Burkhardt quartic, whose tropicalization is a
3-dimensional fan in 39-dimensional space. This effectuates a synthesis of
concrete and abstract approaches to tropical moduli of genus 2 curves.Comment: 33 page
Local and Global Properties of the World
The essence of the method of physics is inseparably connected with the
problem of interplay between local and global properties of the universe. In
the present paper we discuss this interplay as it is present in three major
departments of contemporary physics: general relativity, quantum mechanics and
some attempts at quantizing gravity (especially geometrodynamics and its recent
successors in the form of various pregeometry conceptions). It turns out that
all big interpretative issues involved in this problem point towards the
necessity of changing from the standard space-time geometry to some radically
new, most probably non-local, generalization. We argue that the recent
noncommutative geometry offers attractive possibilities, and gives us a
conceptual insight into its algebraic foundations. Noncommutative spaces are,
in general, non-local, and their applications to physics, known at present,
seem very promising. One would expect that beneath the Planck threshold there
reigns a ``noncommutative pregeometry'', and only when crossing this threshold
the usual space-time geometry emerges.Comment: 43 pages, latex, no figures, changes: authors and abstract added to
the body of pape
Non-commutative geometry of 4-dimensional quantum Hall droplet
We develop the description of non-commutative geometry of the 4-dimensional
quantum Hall fluid's theory proposed recently by Zhang and Hu. The
non-commutative structure of fuzzy appears naturally in this theory.
The fuzzy monopole harmonics, which are the essential elements in this
non-commutative geometry, are explicitly constructed and their obeying the
matrix algebra is obtained. This matrix algebra is associative. We also propose
a fusion scheme of the fuzzy monopole harmonics of the coupling system from
those of the subsystems, and determine the fusion rule in such fusion scheme.
By products, we provide some essential ingredients of the theory of SO(5)
angular momentum. In particular, the explicit expression of the coupling
coefficients, in the theory of SO(5) angular momentum, are given. It is
discussed that some possible applications of our results to the 4-dimensional
quantum Hall system and the matrix brane construction in M-theory.Comment: latex 22 pages, no figures. some references added. some results are
clarifie
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